Elimination of a single Skolem function in pure logic increases the length proofs only linearly. The result is shown for derivations with cuts that are free sequent calculus strong locality property.

Szlachányi’s skew monoidal categories are a well-motivated variation of in which the unitors and associator not required to be natural isomorphisms, but merely transformations particular direction. We present sequent calculus for categories, building on recent formulation by one authors Tamari order (skew semigroup categories). In this calculus, antecedents consist stoup (an optional formula) f...

I formalize important theorems about classical propositional logic in the proof assistant Coq. The main theorems I prove are (1) the soundness and completeness of natural deduction calculus, (2) the equivalence between natural deduction calculus, Hilbert systems and sequent calculus and (3) cut elimination for sequent calculus.

SEQUEL is a new-generation functional programming language, which allows the specification of types in a notation based on the sequent calculus. The sequent calculus notation suffices for the construction of types for type checking and for the specification of arbitrary logics. Compilation techniques derived from both functional and logic programming are used to derive high-performance ATPs fro...